Interacting Random Systems

The group contributes to the following application oriented research topics of WIAS:

Coagulation processes are typical in physics (merging of particles, growth of gas bubbles), meteorology (merging of droplets in clouds, transportation of aerosols), chemistry (hydrogels, formation of aerosols), chemistry (hydrogels, formation of soot), astrophysics (formation of planets). At WIAS, different types of models are investigated: probabilistically with complex Markov processes, analytically with kinetic equations and their properties, numerically with solvability and computational questions for these equations, and heuristically with theoretical descriptions. One of the main questions is under which conditions particularly large particles are formed in large systems, i.e. the occurrence of the gelation phase transition. [>> more]

Many models in statistical physics contain random paths with interactions of various natures, like polymer models, where the path has a self-repellence and attractive interactions with the surrounding medium, or mass transport models in random medium, where the path carries a random mass that is increased and decreased, depending on the properties of the space visited, or self-intersection properties of the path. Also coupled nonlinear diffusion equations are used for modeling such phenomena. [>> more]

Devices in our environment are increasingly networked. The exchange of data in these networks carries both opportunities and risks. Smart devices such as smartphones or self-driving cars play a special role. On the other hand, networks like the Internet of Things are made up of many simple devices. We study random mobile communication networks in terms of fundamental characteristics such as connectivity, capacity, and throughput. The focus is on the investigation of probabilities of extreme system overload, the spread of data in the network and strategies for more efficient data transmission. [>> more]

For more than a hundred years diverse processes and phenomena in the natural sciences have been modelled using random particle systems. At the WIAS macroscopic phenomena in such large systems are analyzed with particular focus on phase transitions such as percolation or gelation. [>> more]

Archive

Further application topics where the institute has expertise in:

These applications are modeled by population balance systems. Accurate and efficient numerical methods will be developed, in collaboration with partners from academics and industry, which will be in the long term the basis of optimal control methods for the considered processes. [>> more]

Research in this field focuses on mathematical aspects of biological evolution through stochastic modelling. The main areas are the effects of complex fitness landscapes on molecular evolution, the study of sexual selection by stochastic modelling of mating preferences and emerging mating patterns, genealogies of the mathematical seed-bank model and mathematical modelling of controlled evolution under experimental conditions. [>> more]